1. Field of the Invention
The present invention relates to a game machine which can have its playing content varied on the basis of a chaos random number produced electronically by chaos random number generating means.
2. Description of Relevant Art
Generally speaking, the pachinko machines using pachinko balls are widely used, pachinko parlor businesses can be seen everywhere, and pachinko is one of the most popular amusements in Japan.
In the pachinko game, the player buys some pachinko balls and shoots them by means of a shooting handle of the machine. If one of the balls lands in a reward catcher, the player is rewarded with more balls. The shooting handle of the pachinko machine in recent years can electromechanically shoot the balls continuously, so that all that is required of the player is to turn the shooting handle. This tend to make the pachinko game monotonous. Thus, in order to make the game more interesting and to reward all players impartially a pachinko machine has been developed and put into practice which is equipped with a game machine incorporating game elements.
This pachinko machine starts the game machine, if predetermined conditions are satisfied, to determine the responses to be taken by the pachinko game so that the player can enjoy more advantageous game conditions. This type of pachinko machine is popular because players can be rewarded with more balls independently of their skills.
Thus, recent pachinko machines have been equipped with more and more CPU control units as electronics technology progresses. Specifically, the game machine incorporated in the pachinko machine is substantially operated by electronics technology, and this operation is controlled by the CPU, i.e., the so-called xe2x80x9cmicroprocessorxe2x80x9d or computer. This computer is assigned a role to compute various pieces of information from the pachinko machine itself or its game machine and to command the pachinko machine to run a predetermined operation according to a predetermined procedure (or program). However, this means mere electronic formatting of the machine, and the player can only await the decision made by the computer.
Along with pachinko machines, a rotary drum type game machine (generally called a xe2x80x98slot machinexe2x80x99 or xe2x80x98pachisloxe2x80x99) having a rotary drum type graphic pattern combining unit has recently grown popular as an amusement. The player of this drum type game machine inserts a coin into the slot and pushes a start button to turn the graphic patterns of the drum so that he or she may be rewarded with more coins according to the combination of the patterns.
This game machine is also equipped with numerous computer control units as a result of the progress of electronics technology. Specifically, the rotary drum type graphic pattern combining unit is also substantially operated by this technology, and this operation is controlled and determined by the computer or microprocessor. The role of this microprocessor is to process various pieces of information obtained from the game machine and the pattern combining unit and to give the game machine a predetermined command in accordance with a predetermined procedure (or program). This results in a monotonous play as in the pachinko machine.
The electronic pachinko machine and drum type game machine described above are extended to have more variety of play than existing game machines. After a little long game, however, the player can determine the responses to be taken by the game machine under predetermined operating situations. This is partly because the responses at the machine side are so simple as to always follow a predetermined procedure or program and partly because the random number producing means used in the computer is of such a low grade that its regularity can be grasped.
On the other hand, the player is a human being and can study the responses of the machine, i.e., the regularity of the random number before long, with the result that he or she will lose interest in the game. In this regard, game parlors are faced with the problem that they are obliged to introduce new game machines at regular intervals.
In order to overcome the disadvantages described above, it is basically sufficient to set the game machines with a computer system having means for producing fine random numbers. As fine random numbers, those generally produced by the linear congruence method or the M-series method are well-known. However, these fine random numbers are difficult for a pachinko machine which uses a relatively inexpensive CPU to produce, as compared a general purpose computer. In other words, a CPU capable of producing fine random numbers is so expensive that it cannot be employed.
Thus, a method for enabling an ordinary CPU to produce fine random numbers easily and variously is greatly desired.
In order to solve the above-specified problems, an object of the present invention is to provide a game machine for providing a game content whose regularity does not easily grasped by the player.
According to a first aspect of the present invention, there is provided a game machine for presenting a game the regularity of which cannot be easily grasped by the player, by making use of chaotic random numbers produced by random number generating means.
According to a second aspect of the present invention, there is provided a pachinko machine comprising: a plurality of reward catchers; sensor means disposed in at least one of the reward catchers for sensing the reward state of the pachinko balls; random number producing means for producing a chaotic random number; and a computer for enabling control of the reward situation of a predetermined one of the reward catchers.
According to a third aspect of the present invention, there is provided a rotary drum type game machine comprising: a rotary type indicator; random number producing means for producing a chaotic random number; and a computer for enabling control of the display of the indicator.
According to a fourth aspect of the present invention, there is provided a game machine wherein a numerical value obtained by solving a nonlinear differential equation is used as one of the conditions for determining the change in the playing content.
According to a fifth aspect of the present invention, there is provided a game machine according to the fourth aspect, wherein the solution obtained from the nonlinear equation has its regularity changed by changing the variable of the equation.
Firstly, what is meant by chaos will be described. A number of predictable phenomena are found in the both natural and artificial worlds. It is possible to predict and respond to Halley""s comet or an artificial satellite. Deterministic predictability providing a clear relation between cause and effect may be one of the greatest powers of science.
However, weather forecasting is deemed the motion of the atmosphere according to physical rules, but is often false. Phenomena having an unclear connection between cause and effect is thought to have complex elements which would be accurately predictable if the complete parameters describing the system are known, that is, if sufficient information on the system can be collected.
In short, random properties are thought to arise from shortage of information on the system having multiple degrees of freedom. However, by the discovery that even a simple system having a smaller number (e.g., three or more) of degrees of freedom may exhibit random behavior, it has been found that there are some phenomena which are deterministic but essentially random. These random properties are called xe2x80x9cchaosxe2x80x9d.
However, the concept of chaos is not yet integrated. Like the theory of evolution, the definition of chaos spreads over a wide range, and its concept seems to stand alone depending on the object. Therefore, chaos is defined as the following for the purposes of this specification.
Chaos means the phenomenon which is a system having deterministic rules but extremely complex nonlinear behavior, such that it is essentially random. Moreover, phenomena which apparently have no regularity, no predictability and an absence of order, are backed by complicated order or regularity.
Extremely fine random numbers can be produced by applying this concept of chaos to mathematics to solve a specific nonlinear equation. As an example of these random numbers, the following one-dimensional nonlinear differential equation, as expressed by mapping r from one to another section, may have an irregular and random solution called chaos:
Xn+1=r(Xn), n=0,1,xe2x80x83xe2x80x83(1)
This simple nonlinear mapping is exemplified by the Bernoulli shift, logistic mapping, tent mapping or Tshebyscheff mapping.
For example, the Bernoulli shift is expressed by the following equation:
r(Xn)=2Xn, 0xe2x89xa6Xnxe2x89xa6xc2xd
r(Xn)=2Xnxe2x88x921, xc2xdxe2x89xa6Xnxe2x89xa61xe2x80x83xe2x80x83(2)
Logistic mapping is expressed by the following equation:
r(Xn)=bXn(1xe2x88x92Xn)xe2x80x83xe2x80x83(3)
For b=4.0 in this Equation 3, chaos is referred to as xe2x80x9cpure chaosxe2x80x9d.
On the other hand, tent mapping is expressed by the following equation:
r(Xn)=Xn/xcex8, 0xe2x89xa6Xnxe2x89xa6xcex8
r(Xn)=(1xe2x88x92Xn)/(1xe2x88x92xcex8), xcex8xe2x89xa6Xnxe2x89xa61xe2x80x83xe2x80x83(4)
Tshebyscheff mapping is expressed by the following equation:
r(Xn)=cos (n cosxe2x88x921Xn)xe2x80x83xe2x80x83(5)
The solutions of these equations are individually chaos random numbers, the regularity of which is usually unclear. Chaotic random numbers other than those mappings could be produced.
As the variable b in the logistic mapping equation is changed, for example, the solution obtainable changes within the range from 0.0 to 1.0 as the variable b approaches 4, such that it approaches more chaotic random numbers. If this variable is altered, on the other hand, the obtainable solution can be limited such that the solution converges to one for b=2 and to four for b=about 3.5. As the variable b approaches 4, that limit is reduced so that the solution takes the value of a chaotic random number within a predetermined range.
This behavior is shown in FIG. 3. FIG. 3 illustrates the value of the solution of logistic mapping, which is obtained from Equation 3 for n=300 to 500 when an initial value Xo is set at 0.3 and when the variable b is changed from 0 to 4. The value of the ordinate corresponding to the position of a black dot appearing in FIG. 3 is the value of the solution. As described above, the solution converges to one if the value b is smaller than about 3, and to two if the value b is around 3.1 to 3.4. As the value b increases, the solution increases to four, eight and so on so that the targets of convergence increase to gradually take the values of chaotic random numbers.
However, during the repetition of calculations for b=4, for example, the solution may be 0.5 after a predetermined number of repetitions dependent upon the significant digits for the operations. After this, all the solutions are 0.5. Thus, the solutions may depart from chaotic random numbers unless care is taken as to how to take the significant digits for the operations and the range of repetitions making use of the solutions.
The game machine of the present invention is constructed by making use of the chaotic random numbers thus produced by the aforementioned method. This game machine is constructed to comprise a random number producer capable of producing the aforementioned chaotic random numbers, a computer unit for issuing various instructions according to the random numbers produced by that producer, and a unit for changing the responses of the game in accordance with the instructions of the computer. Thus, the player can be kept unacquainted with the content of the game.
In case of the pachinko machine, for example, the player starts the play so that a safe ball lands in a reward catcher. The safe ball detecting means defects the safe ball and electronically produces a chaotic random number. Then, the catching states or the like of the safe ball catcher on the playing board are controlled on the basis of the electronically produced chaotic random number.
As described above, on the other hand, the solutions can be limited by changing the variable of the equation so that production of the random number can be controlled.
Specifically, the variable is incorporated into part of the playing conditions, and the solution of the aforementioned equation is determined under that condition so that the play content is modified by the solution. Thus, when the play content is modified according to the solution of the equation, the response of the game machine at the time of a specific variable and the response at the time of another variable can be made different to provide a more complicated game.
Alternatively, the solution of the equation could be other than random numbers. In order to realize conditions suitable for a beginner or advantageous for a player, the difficulty level of the game can be changed to complicate or simplify the play content by changing the variable to a predetermined value to set a state, in which the solution of the equation is liable to issue a specific numerical value, thereby setting a play content advantageous to the player.
The present invention can be applied to a pachinko machine which comprises a variable display device in which display of a symbol such as numeral, character and design and the like is renewed according to entrance of a ball into a specific prize-winning port provided on a board of the pachinko machine; means for producing a chaos random number; and a control means for controlling a renewing period of the display of the variable display device based on the chaos random number.
Also, the present invention can be applied to a pachinko machine which comprises a variable display device in which a plurality of displays of symbols such as numeral, character and design and the like are renewed according to entrance of a ball into a specific prize-winning port provided on a board of the pachinko machine; means for producing chaos random numbers plural times; and a control means for controlling renewing periods of the plurality of displays of the variable display device based on the chaos random numbers, respectively. The renewing period(s) of the variable display device is varied based on the chaos random number by a computer to make it difficult for a player to find a response of the machine.
For example, when a game ball is entered into a specific prize-winning port in play by a player, whether the entrance is big hit or failure is determined based on a signal reflecting the game ball entrance, and the display of the variable display device is determined to start renewal of the display. A time when the display is stopped is determined based on a chaos random number produced by the chaos random number production means, and the aimed display is displayed in order on the device after a set time has passed.
As described above, on the other hand, the solutions can be limited by changing the variable of the equation so that production of the random number can be controlled.
Specifically, the variable is incorporated into part of the playing conditions, and the solution of the aforementioned equation is determined under that condition to vary the renewing period according to the solution. Thus, when the renewing period is varied according to the solution of the equation, the response of the game machine at the time of a specific variable and the response at the time of another variable can be made different to provide a more complicated game.